第2367题：积分练习

解 $\int \dfrac{x^2}{(x-1)^{30}}dx$ .

A. $\dfrac{1}{27(x-1)^{27}}$ $+\dfrac{1}{14(x-1)^{28}}$ $+\dfrac{1}{29(x-1)^{29}}+C$

B. $\dfrac{1}{27(1-x)^{27}}$ $-\dfrac{1}{14(1-x)^{28}}$$+\dfrac{1}{29(1-x)^{29}}+C$

C. $\dfrac{1}{x-1}$ $+ \dfrac{1}{2(x-1)^2}$ $+\dfrac{1}{3(x-1)^3}$ $+\cdots+\dfrac{1}{29(1-x)^{29}}+C$

D. $-\dfrac{1}{x-1}$ $+ \dfrac{1}{2(x-1)^2}$$-\dfrac{1}{3(x-1)^3}$ $+\cdots$$-\dfrac{1}{29(1-x)^{29}}+C$

提示：$x=x-1+1$ .